# 3) What is wrong with the following proof that all horses have the same color? Let...

###### Question:

3) What is wrong with the following proof that all horses have the same color? Let P(n) be the proposition that all the horses in a set of n horses are the same color. Clearly, P(1) is true. Now assume that P(n) is true. That is, assume that all the horses in any set of n horses are the same color Consider any n1 horses; number these as horses 1,2,3,...,n,n +1. Now the first n of these horses all must have the same color, and the last n of these must also have the same color. Since the set of the first n horses and the set of the last n horses overlap, all n 1 must be the same color This shows that P(n+ 1) is true and finishes the proof by induction.

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